Dynamic response of a rotating ball screw subject to a moving regenerative force in grinding

This paper investigates the dynamic response of a rotating ball screw subjected to a moving regenerative force. The rotating ball screw is modeled as a rotating Timoshenko shaft with simply supports. The moving regenerative force describes the nonlinear interactions including the effects of wheel wear, time-delay, and the possibility of contact loss between the grinding wheel head and screw. The assumed mode method together with Runge–Kutta method is employed to analyze the system dynamic response. The total grinding depth is suggested to divide into several passes from rough grinding to fine grinding for obtaining fine surface. The effect of parameters such as the depth of cut and the rotational speeds of grinding wheel and screw are discussed for each pass. The numerical results show that the critical depth of cut depends on the rotational speeds of screw and grinding wheel. If the more the depth of cut is smaller than the critical depth of cut, the earlier the chatter occurs and the faster the vibration grows.     

Generalized thermoelastic infinite medium with spherical cavity subjected to moving heat source

This paper deals with a problem of thermoelastic interactions in an isotropic unbounded medium with spherical cavity due to the presence of moving heat sources in the context of the linear theory of generalized thermoelasticity with one relaxation time. The governing equations are expressed in the Laplace transform domain and solved in that domain. The inversion of the Laplace transform is done numerically using the Riemann-sum approximation method. The numerical estimates of the displacement, temperature, stress, and strain are obtained for a hypothetical material. The results obtained are presented graphically to show the effect of the heat source velocity and the relaxation time parameters on displacement, temperature, stress, and strain.     

Laminar boundary layers along an infinite porous plate in the presence of a transverse magnetic field

Exact solutions of the Navier-Stokes equations are derived by a Laplace-transform technique for two-dimensional, incompressible flow of an electrically conducting fluid past on infinite porous plate. It is assumed that the flow is independent of the distance parallel to the plate and that the velocity component normal to the plate is constant. A general formula is derived for the velocity distribution in terms of the given external velocity. The skin friction is obtained and some special cases are considered.     

The response of a thin elastic plate to a moving pressure point

Zusammenfassung Eine dünne unendliche elastische Platte sei plötzlich durch einen in einem Punkt konzentrierten Druck belastet, der sich danach auf einer Geraden mit konstanter Geschwindigkeitc bewegt. Unter Anwendung der elementaren Plattentheorie wird eine Integraldarstellung der Verbiegung hergeleitet. Dieses Integral kann in besonderen Fällen ausgewertet werden, insbesondere am Nullpunkt und unterhalb der sich bewegenden Last. Asymptotische Ergebnisse zeigen an, dass längs der Bahn des Druckpunktes grosse Plattenverbiegungen zu erwarten sind. Schliesslich wird die Lösung für die stationäre Punktbelastung als Grenzlösung des allgemeinen nicht-stationären Problems gefunden.

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Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force under AFOSR Grant No. 821-65.     

Group solution for unsteady free-convection flow from a vertical moving plate subjected to constant heat flux

The problem of heat and mass transfer in an unsteady free-convection flow over a continuous moving vertical sheet in an ambient fluid is investigated for constant heat flux using the group theoretical method. The nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effect of Prandlt number on the velocity and temperature of the boundary-layer is plotted in curves. A comparison with previous work is presented.     

On unsteady flow of an infinite expanse of a visco-elastic Maxwell liquid bounded by a flat plate under the influence of an impulsive force

The equations of motion of the title problem are solved using Laplace transforms.     

Mathematical modeling of a thin viscous layer adhering to an infinite plate withdrawn at an angle

We consider the problem of a thin viscous layer adhering to an inclined plate. Systems of boundary-layer equations and capillary-statics equations are used. The solutions of the two systems are matched at a certain point, which ensures a smooth profile of the free surface of the liquid.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 73, pp. 57–61, 1992.     

Steady flow of a second-order thermo-viscous fluid over an infinite plate

The steady flow of a second-order thermo-viscous fluids over a moving infinite flat plate is examined. It is observed that in the absence of any body force in the flow region, a constant temperature gradient is generated, which depends upon the plate velocity and material constants. The mean velocity, mean bulk temperature and Nusselt number are calculated.     

Numerical study of a transverse streamlined flow of an infinite series of cylinders

The problem of transverse streamlined flow of an infinite series of cylinders by a flow of viscous incompressible liquid is considered. The problem is solved numerically by using the method of difference approximation of the Navier-Stokes equations with use of Arakawa scheme of the second degree of accuracy. Computations were given for a series of cylinders with the step L=2.2, 2.8, 3.2, 3.6 and with Reynolds numbers Re equal to 40, 100, 200, 400. Relations between the hydrodynamic characteristics of the series and the distance between the axes of the cylinders are obtained for different Reynolds numbers.Translated from Dinamicheskie Sistemy, No. 7, pp. 53–57, 1988.     

Exact solutions for the flow of an Oldroyd-B fluid due to an infinite flat plate

The unsteady flow of an Oldroyd-B fluid due to an infinite flat plate, subject to a translation motion of linear time-dependent velocity in its plane, is studied by means of the Laplace transform. The velocity field and the associated tangential stress corresponding to the flow induced by the constantly accelerating plate as well as those produced by the impulsive motion of the plate are obtained as special cases. The solutions that have been determined, in all accordance with the solutions established using the Fourier transform, reduce to those for a Newtonian fluid as a limiting case. The similar solutions for a Maxwell fluid are also obtained.     

Fundamental elastic field in an infinite plane of two-dimensional piezoelectric quasicrystal subjected to multi-physics loads

By utilizing the extended Stroh formalism, the Green's function of infinite plane is obtained for the problem of two-dimensional decagonal quasicrystals with the piezoelectric effect subjected to multi-physics loads. By numerical computations, the piezoelectric effect of the two-dimensional decagonal quasicrystals is revealed; the changes of the stress and displacement fields with multi-physics loads are discussed. The variation laws of material constants in stress and displacement fields are investigated. The results show that the effect of the phason field on the generalized displacement is larger than that on the generalized stress; and the effects of material parameters are different in diverse field.     

Global bifurcations and single‐pulse homoclinic orbits of a plate subjected to the transverse and in‐plane excitations

The Shilnikov‐type single‐pulse homoclinic orbits and chaotic dynamics of a simply supported truss core sandwich plate subjected to the transverse and the in‐plane excitations are investigated in detail. The resonant case considered here is principal parametric resonance and 1:2 internal resonance. Based on the normal form theory, the desired form for the global perturbation method is obtained. By using the global perturbation method developed by Kovacic and Wiggins, explicit sufficient conditions for the existence of a Shilnikov‐type homoclinic orbit are obtained, which implies that chaotic motions may occur for this class of truss core sandwich plate in the sense of Smale horseshoes. Numerical results obtained by using the fourth‐order Runge–Kutta method agree with theoretical analysis at least qualitatively. Copyright © 2017 John Wiley & Sons, Ltd.     

Dynamic response of a stratified transversely isotropic half-space with a poroelastic interlayer due to a buried moving source

Response of a ground subjected to dynamic sources is a classical problem in many fields. This paper develops a transversely isotropic (TI) half-space ground model which considers the alternating distribution of different media: a TI elastic surface layer, a TI poroelastic interlayer and a TI elastic half-space from top to bottom. The model can consider soils with different properties and the existence of groundwater. Dynamic responses of the model subjected to a buried moving source are investigated. General solutions to the TI poroelastic interlayer in the wavenumber domain are derived by Fourier transform and a potential function method in a Cartesian coordinate system. The layered system with different media is solved adopting an ‘adapted stiffness matrix method’ for a buried source scenario. Dynamic responses in the time-spatial domain are obtained by inverse fast Fourier transform (iFFT) and numerical integration. The performance of the method in this study is first tested by comparison with existing research, and the influences of the existence of pore water in the interlayer, transverse isotropy, and source features are comprehensively investigated. The effect of pore water is more significant for a TI ground compared with isotropic ground, and the model in this study cannot be simplified by an ‘equivalent’ layered TI elastic model. Peak values of displacement and pore pressure exist with increasing source speed. Source speeds corresponding to them are related to the wave speeds of the medium and affected by transverse isotropy.     

Boundary layer growth of an infinite flat plate in magnetohydrodynamics

Zusammenfassung Eine genaue Formel wird abgeleitet für die gesamte Scherkraft, die durch impulsive Bewegung einer unendlichen flachen Platte einer zähen, nichtzusammendrückbaren und elektrisch leitenden Flüssigkeit im Bereich eines äusseren Magnetfeldes verursacht wird. Dazu werden Laplace-Transformationen gebraucht. Für die Geschwindigkeitsverteilungen und das Magnetfeld werden die Formeln gefunden. Zwei Fälle werden untersucht: 1. die Platte ist nichtleitend; 2. die Platte ist vollständig leitend. Für lange Zeitent wird die Geschwindigkeitsverteilung als Hartmann-Profil festgestellt.     

Stability loss in an infinite plate with a circular inclusion under uniaxial tension

Loss of stability under uniaxial tension in an infinite plate with a circular inclusion made of another material is analyzed. The influence exerted by the elastic modulus of the inclusion on the critical load is examined. The minimum eigenvalue corresponding to the first critical load is found by applying the variational principle. The computations are performed in Maple and are compared with results obtained with the finite element method in ANSYS 13.1. The computations show that the instability modes are different when the inclusion is softer than the plate and when the inclusion is stiffer than the plate. As the Young’s modulus of the inclusion approaches that of the plate, the critical load increases substantially. When these moduli coincide, stability loss is not possible.     

Dynamic response of cable-stayed bridges to moving vehicles using the structural impedance method

The importance of dynamic interactions between cable-stayed bridges and heavy moving vehicles, such as trucks and locomotives, has been recognised by bridge engineers for a long time. A structural impedance algorithm is developed for analysing the dynamic response of cable-stayed bridges subjected to traversing vehicles. The bridge deck is modelled as an elastic plate, and the cables are idealised as springs for simplicity. The vehicles are modelled as a series of masses with suspension systems moving with different speeds and accelerations. A comprehensive computer program, CABLESIM, is developed for the static and dynamic analyses of a cable-stayed bridge. The accuracy of the numerical procedure and its computer implementation is verified with the available analytical and experimental results. A parametric study is conducted to investigate the effects of vehicle velocity, girder depth, different types of cable arrangements, and traffic load on the dynamic response of the deck. The numerical results are expected to be important in assessing the dynamics of cable-stayed bridge components and in determining the safety and allowable traffic conditions.